Thursday, February 02, 2012

Q: Write the digits from 1 to 9 in a line. If you put a plus sign after the 2, a times sign after the 4, and plus signs after the 6 and 8, the line shows 12 + 34 x 56 + 78 + 9, which equals 2003. That's nine years off from our current year 2012. This example uses four arithmetic symbols. The object is to use just three of the following arithmetic operations: addition, subtraction, multiplication and division, in a line from 1 to 9 to get 2012 exactly. The operations should be performed in order from left to right. There are no tricks to this puzzle. Can you do it?

I was just about to retire for the evening, but I figured you might need some assistance in solving the puzzle, so your help is... Gee, how do I give you a hint to a math puzzle?

Edit: The hints were "retire" (Social Security Administration = SSA = subtract, subtract, add) and "assistance" and "help" (411 = number of digits to group together, with 3 being assumed for the remaining digits).

56 comments:

Here's my standard reminder... don't post the answer or any hints that could lead directly to the answer (e.g. via Google or Bing) before the deadline of Thursday at 3pm ET. If you know the answer, click the link and submit it to NPR, but don't give it away here.

You may provide indirect hints to the answer to show you know it, but make sure they don't give the answer away. You can openly discuss your hints and the answer after the Thursday deadline. Thank you.

As our resident anal mathematician, I will point out that saying the operations should be performed in order from left to right is not actually correct, as Will's example demonstrates.

If we were to actually perform the operations from left to right, then 12 + 34 x 56 + 78 + 9 would be calculated as {[(12 + 34) x 56] + 78} + 9, which equals 2663, not 2003.

Obviously Will intends for us to follow the traditional mathematical order of operations, wherein we first calculate multiplication and division from left to right, and then addition and subtraction from left to right with what remains.

However, the common mnemonic PEMDAS can be somewhat misleading since multiplication has equal weight to division, and addition has equal weight to subtraction. So, for instance, if given a line like 12/3*4, it is best interpreted as (12/3)*4 = 16, not as 12/(3*4) = 1.

I agree with PC that the usual order of precedence among arithmetic operators contradicts Will's phrasing of the puzzle. However, there is only one answer to this puzzle and it does follow both the ordering of computations that Will stated and the usual operator precedence.

I can see why Blaine might have been a little concerned about your deleted post, but I think what you posted was said by Will and shown clearly in his example. I found none of the posts at all helpful, and some very misleading. I may say more on Thursday.

If I may get back to the topic of LAST WEEK's challenge, I had tried many times to post my submissions here but I couldn't get past that blasted word verification. I STILL wonder how ANYBODY was able to post any comments last week at this time!!

Anyway, I'm glad that Blaine has fixed it, so here are the three entries I submitted last week:

My entries: 1. When Things Were Rotten - Then Came Bronson - Pushing Daisies - Six Feet Under2. It Takes a Thief - To Catch a Predator - In the Heat of the Night - When Animals Attack3. According to Jim - The King Family Show - Real People - Good Times - Until Tomorrow

And in 10 years, when Will will have been the NPR puzzlemaster for 35 years, 1234 + 5 - 6 + 789 = 2022. I'm a bit surprised that Blaine let me get away with such a broad hint that there was a "-5" term in there.

My minimalist answer to this puzzle involves moving one digit of the example. Move the 8 from next to the 7 to theother side of the + and put it next to the 9. The sample was 12 + 34x56 + 78 + 9 = 2003.The result is 12 + 34x56 + 7 + 89 = 2012.

Honestly do they think that NPR listeners don't remember the precedence of mathematical operators? It wasn't necessary to say left to right. This week's puzzle works left to right or using precedence of mathematical operators (where plus and minus have the same precedence so you would go left to right anyway). Will should just stick to words since numbers are obviously not his forte.

Here! Here! SDB. I skipped this week's puzzle and had chocolate martinis (well only one really)instead. I was leaning toward EKW's solution, kept wanting that 12 to stay intact. I should have paid more attention to Tommy Boy's "Take Five".

I'm very disappointed....I heard this when first broadcast, and decided to write a computer program to come up with the answer...Cheating you may say, but not really. I thought it would be a good exercise for expanding my Python skills. Anyway, the program I wrote assumed that the words, "use just THREE of the following arithmetic operations: addition, subtraction, multiplication and division", meant, well, use three. The answer only uses two. Did no one else find that misleading?

I read it as 3 operators from the four basic operators where they might be the same. Reinforcing this idea is the example which uses 4 operators (but only two unique ones). So I didn't read it as 3 different operators... but as 3 exactly with repeats allowed.